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B-spline is extensively used for the solution of many physical models appearing in the fields of plasma physics, fluid mechanics, atmosphere-ocean dynamics and many other disciplines. In this article, Riesz space fractional PDEs (RSF-PDEs) in two forms are solved by using hybrid B-spline collocation method (HBCM). In the given methodology, RSF-PDEs are discretized into the system of algebraic linear equations by using hybrid B-spline basis function. The resultant system is solved by a numerical technique. The Von Neumann stability analysis method is used for analyzing the stability of proposed method. Numerical experiments are conducted to illustrate the accuracy of proposed method, by representing the results graphically and numerically for different values of fractional parameters.